Confidence Regions for Parameters in Stationary Time Series Models With Gaussian Noise

Frontiers in Physics

Zhiping Lu¹  Riquan Zhang¹  Xiuzhen Zhang² 

[1] Key Laboratory of Advanced Theory and Application in Statistics and Data Science, MOE, School of Statistics, East China Normal University, Shanghai, China;School of Mathematics and Statistics, Shanxi Datong University, Datong, China;

关键词: confidence region;    adjusted empirical likelihood;    mean empirical likelihood;    stationary time series;    long memory;   

DOI  :  10.3389/fphy.2021.801692

来源: DOAJ

【 摘 要 】

This article develops two new empirical likelihood methods for long-memory time series models based on adjusted empirical likelihood and mean empirical likelihood. By application of Whittle likelihood, one obtains a score function that can be viewed as the estimating equation of the parameters of the long-memory time series model. An empirical likelihood ratio is obtained which is shown to be asymptotically chi-square distributed. It can be used to construct confidence regions. By adding pseudo samples, we simultaneously eliminate the non-definition of the original empirical likelihood and enhance the coverage probability. Finite sample properties of the empirical likelihood confidence regions are explored through Monte Carlo simulation, and some real data applications are carried out.

【 授权许可】

Unknown